TỔNG HỢP CÁC BÁO CÁO KHOA HỌC VỀ CUNG CẤP ĐIỆN CỦA BỘ MÔN HỆ THỐNG ĐIỆN (ĐẠI HỌC BÁCH KHOA HÀ NỘI)

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IEEE TRANSACTIONS ON POWERDELIVERY, VOL. 23, NO. 1, JANUARY 2008 347
Fault Distribution Modeling Using Stochastic
Bivariate Models for Prediction of Voltage
Sag inDistribution Systems
Bach Quoc Khanh, Dong-Jun Won, Member, IEEE, and Seung-Il Moon, Member, IEEE
Abstract—This paper presents a new method regarding fault dis-
tribution modeling for the stochasticprediction study of voltage
sags in the distribution system. 2-D stochastic models for fault mod-
eling make it possible to obtain the fault performance for the whole
system of interest, which helps to obtain not only sag performance
at individual locations but also system sag performance through
system indices of voltagesag. By using the bivariate normal dis-
tribution for fault distribu
ti
on modeling,this paper estimates the

influence of model parameters on system voltagesag performance.
The paper also develops the modified
regarding phase
loads that create better estimation for voltagesag performance for
the distribution system.
Index Terms—Bivariate normal distribution, distribution
system, fault distribution modeling, phase loads, power quality
(PQ), stochasticprediction, voltagesag frequency.
I. INTRODUCTION
A
MONG power-quality (PQ) phenomena, the voltage sag
(dip) is defined inIEEE1159, 1995 as a decrease in rms
voltage to between 0.1 and 0.9 of the nominal voltage at the
power frequency for the duration of 0.5 cycle to 1 min. There has
been a greater interest in voltage sags recently due to problems
caused by the performance of sensitive electronic equipment
that iswidely used.
Research about the voltage sag is usually related to a basic
process known as a “compatibility assessment” [1], [2] which
includes three steps.
Step 1) Obtain the voltage sag performance of the system of
interest.
Step 2) Obtain equipment voltage tolerance.
Step 3) Compare equipment voltage tolerance with the
voltage sag performance and estimate the expected
impacts of the voltage sag on the equipment.
Current research has shown evidence that obtaining
the
v
oltage sag performance still needs more improvement. The

Manuscript received August 2, 2005; revised December 5, 2006. This work
was supported by the Korea Foundation for Advanced Studies’ International
Scholar Exchange Fellowship for the academic year of 2004–2005. Paper no.
TPWRD-00456-2005.
B. Q. Khanh iswith the Electric Power System Department, Faculty of Elec-
trical Engineering, Hanoi University of Technology, Hanoi,Vietnam (e-mail:
).
D J. Won iswith the School of Electrical Engineering,
INHA Univ
ersity,
Incheon 402–751, Korea (e-mail: ).
S I. Moon iswith the School of Electrical Engineering and Computer Sci-
ence, Seoul National University, Seoul 151-742, Korea (e-mail: moonsi@plaza.
snu.ac.kr).
Digital Object Identifier 10.1109/TPWRD.2007.905817
information about the voltage sag ismainly obtained by
monitoring and stochastic prediction. With recently advanced
computer-aided simulation tools, the stochastic prediction of
voltage sag becomes the preferable approach that can obtain
the results at required accuracy for various network topologies
and operational conditions.“The method of fault positions”
and “the method of critical distances” are known as the most
widely used methods for stochastic prediction studies.
It is notable that regardless of which method is used, a sto-
chastic prediction study always has to solve two critical
prob-
lems
: 1) the modeling of causes leading to voltage sags and
2) the simulation of the power system for computing voltage sag
characteristics. Among important cause of voltage sags, short-

circuit faults in the power system account for the largest part and
the assessment of the voltage sag performance based on fault
distribution modeling is a well-known approach. However, it is
very difficult to build up “accurate” fault modeling because the
data of faults can only obtained by monitoring and, thus, it has
the same uncertainties as to what the monitoring of voltage sags
can generate.
This paper presents a new approach on fault distribution mod-
eling for the stochastic prediction of voltage sags in the distri-
bu
ti
on system using the method of fault positions. The simula-
tion of the distribution system and fault distribution modeling
are made on MATLAB for computing not only site indices, but
also system indices of voltage sags.
II.F
AUL T DISTRIBUTION MODELING
Modeling the fault distribution is to determine the short-cir-
cuit fault frequency (i.e., fault rate or the number of short-circuit
faults per year) for all fault types at all possible fault positions
throughout the system of interest. It consists of the selection of
fault position and fault type and the distribution of fault rate for
the selected fault positions and fault types.
Fault positions are generally chosen in a way that a fault po-
sition should represent short-circuit faults leading to sags with
similar characteristics [2].For the distribution system with typ-
ical radial
network topology, small line segments, and distribu-
t
ion transformers along the trunk feeders, it is possible to apply

only one fault position for each distribution transformer and one
fault position for each line segment.
Different fault types should be applied to each fault position
mainly depending on the number of phases available at the se-
lected fault positions. The fault rate of each fault type is nor-
mally referred from the observed historical data.
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The fault rate mainly depends on fault position, fault type,
and fault cause. While two earlier factors have been discussed
at length in past research, the distribution of the fault rate for
the selected fault positions has received less interest. The most
common assumption that has been argued so far is that because
the fault can occur anywhere in the system, stochastically, it is
possible to model the fault rate as the uniform distribution [3],
[4]. In this sense, the fault rate at each position is identical to
the component failure rate that is based on component relia-
bility. However, in reality, many factors can lead to faults, not
just the component failure, and fault rates at different positions
in
the
system are rarely the same. Recently, a report [5] pro-
posed some interesting 1-D models of fault distribution along
individual line segments (between two nodes). However, this re-
search could not consider the distribution of transformer faults.
Furthermore, by using 1-D fault distribution, it is hard to ob-

tain a system index about voltage sag performance since there
are plenty of line segments in the distribution system. The new
method of fault distribution modeling proposed by this paper
carefully analyzes concerned fault causes and builds up a suit-
able modeling of the fault distribution for the whole system of
interest
from which system i
ndices can be obtained.
III. N
EW FAULT DISTRIBUTION MODELING BASED
ON
FAUL T CAUSES FOR DISTRIBUTION SYSTEMS
Although there are a variety of causes that result in faults in
distribution systems, it is possible to group them into two parts:
namely 1) equipment failures and 2) external causes.
Equipment failure is basically due to defects that are prob-
ably created during manufacture, transportation, and installa-
tion.Equipment failure depends on the time of being placed
into operation, the aging period, and maintenance conditions.
According to the reliability theory, it is often characterized by
the component failure rate. There are several distribution func-
tions
to model this parameter but the most common one i
s the
exponential distribution which assumes the component failure
rate to be constant. This value is equal to the average failure
rate during the useful life of the “bathtub” curve [6]. Therefore,
if the same type of equipment is used throughout the system
(e.g., the same type of distribution transformers used in the dis-
tribution system), it is possible to assume that the failure rate

of equipment follows the uniform distribution depending on the
equipment type although itstill may cause some errors (e.g., not
all equipment is put into
operation at the same time or has the
same
maintenance conditions).
Besides equipment failure, there are many other causes from
the ambient environment that also may lead to faults in power
systems. This paper calls them the external causes. Some can in-
fluence the fault performance of the power system in a large area
such as severe weather (wind storms, lightning, etc.). Mean-
while, others mainly have local impacts, such as trees and ani-
mals (birds, mice, etc.). Human factors (scheduled interruption,
human errors, mischief, and vandalism) can cause faults that
only influence the power system in small parts as well as se-
vere faults for a large power system. All of these causes occur
randomly and they can be simulated by stochastic models. 1-D
stochastic models seem to not be suitable as explained
before.
Fig. 1.Example of bivariate normal distribution.
This paper proposes the idea of using 2-D stochastic models in-
stead (e.g., the bivariate normal distribution model as illustrated
in Fig. 1).
For large power systems, it is hard to obtain a converged 2-D
fault distribution model for various causes in a large area. How-
ever, for small-to-medium-size networks, such as the section of
distribution network fed from a bulk-point distribution substa-
tion, of which the monitored historical data of fault performance
shows that faults due to external causes occur concentratively on
one location (e.g., some lines pass through a small area which

isa
thi
gh risk for faults due to industrial pollution or trunk fall),
it is the favorite condition to obtain a converged 2-D fault dis-
tribution model.
IV. P
ROBLEM DEFINITION AND SOLUTION
A. Case Study Definition
To illustrate the new method of fault distribution modeling
in the stochastic prediction of voltage sag in the distribution
system, this paper uses the IEEE 123-bus radial distribution
feeder [7] as the test system. It can be seen as the distribution
system is fed from a bulk point. It does not narrow the scope of
application of the study with the following assumptions.
•Since line segments in the test system come in one, two,
and three phases, distribution transformers at load nodes
are the single phase type for separate single-phase loads.
For three-phase loads, the connection of the distribu
-
t
ion transformer is4.16-kV grounded wye—low-voltage
grounded wye.
• Voltage sags are only caused by faults in the test system.
• If the test system is supposedly a section of a large distri-
bution system, only faults occurring in it are considered.
The faults in sections fed from other distribution substa-
tions can be skipped as the transformer impedance indis-
tribution substations, in reality, is rather high. Similarly, the
faults in low-voltage networks are also ignored because of
the large impedance of distribution transformers. This as-

sumption only neglects voltage sags caused by faults in
the
transm
ission system. It will be considered if the stochastic
prediction of voltage sag in large transmission systems [4]
is included.
• In terms of reliability, the test system is modeled on two
main components: lines and distribution transformers. The
reliability of any other distribution equipment is suppos-
edly included in the reliability of these two components.
• The fault positions are selected as mentioned in Part II.For
transformers, one fault position
at each load node (i.e., the
nodes
connected with distribution transformers) is applied.
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KHANH et al.:FAULT DISTRIBUTION MODELING USING STOCHASTIC BIVARIATE MODELS 349
For lines, one fault position is also applied for each line
segment. Due to the short line segments, this paper selects
the fault position at the end of each line segment (For the
test system, there are 122 line segments and 87 load nodes.
Therefore, 209 fault positions in total are selected).
• Fault types (single phase to ground, phase to phase, two
phases to ground, and three phases to ground) are applied
to fault positions depending on the number of available
phases. The fault impedance is assumed to be negligible.
• The fault rate of a distribution transformer is a random

variable depending on the position of the load node it is
connected to. The fault rate of a line segment is also a
random variable
depending on the fault position and the
length
of thisline segment.
Based on the previous definitions and assumptions, the com-
putation of voltage sags at all load nodes on the primary side
of distribution transformers throughout the test system is per-
formed on MATLAB [8]. The voltage sag frequency at each load
node is obtained when applying the fault rate to each fault posi-
tion. The fault rates at the fault positions are calculated based on
the new fault distribution modeling presented in Part B.Finally,
related voltage sag indices are calculated.
B. Fault-Rate Modeling
Faults are random events and as previously indicated, they
can be simulated by stochasticdistribution models. Accord
ing
to the analysis in Section III, the fault rate of each fault type at
each fault position is equal to the sum of equipment failure rate
and fault rate due to external causes. The equipment failure rate
is supposed to follow the uniform distribution model. Therefore,
for the fault position of the transformer
, the failure rate is cal-
culated as follows:
(1)
where
number of transformer faults of the test system;
total distribution transformers;
contributory percentage of equipment failure.

The line failure rate is normally expressed in the number of
faults per year per foot (or meter) length. However, because of
the short length of line segments, the line failure rate is calcu-
lated for the whole line segment
as follows:
(2)
where
number of line faults of the test system;
total line segments;
length of the line segment (in feet).
The distribution of the fault rate due to external causes de-
pending on fault positions is supposedly in compliance with the
2-D stochastic model. This paper uses bivariate normal distribu-
tion because it is the most common stochastic model which has
such critical advantages as it accepts continuous variables and is
easy to build up the distribution based on monitored historical
data. Besides that, it is also simple to convert to other models
using continuous variables.
So the fault rate at each fault position is
as follows.
For
the transformer
(3)
For the line segment
(4)
where
contributory percentage of faults due
to external causes
;
, weighted factors of the fault rates of

the transformer
and the line segment
that follow the bivariate normal
distribution model depending on fault
positions.
The joint probability density function of bivariate normal dis-
tribution is expressed as follows:
where
(5)
, , , means and standard deviations of two
variables
, ;
correlation coefficient. If the
coordinates of fault positions are
independent variables
.
The probability for a fault to occur at the fault position
within an area can be calculated as follows:
(6)
If
and is large enough,
then the distribution is normalized as follows:
(7)
For the distribution system, geographically, if network nodes
are disposed relatively uniform, itwill be possible to apply the
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following approximation where and are the coordinates of
the fault position
.
• Faults rate for the transformer
(8)
• Fault rate for the line segment
(9)
C. Development of Voltage Sag Indices
PQ indices are used to estimate the quality of supplied elec-
tric energy for the power system. To date, many PQ indices
have been proposed for various PQ events. A well-known index
of voltage sag is the system average rms voltage variation fre-
quency index for voltage sag down to under X% of the nominal
voltage value
. It is often used for evaluating the PQ
of a three-phase power system based on monitored limited seg-
mentation [3]. The assessed system is segmented so that every
point in the system is contained within a section monitored by
an actual PQ measuring instrument.
In distribution systems, because various phase loads (phase
to neutral, phase to phase, three-phase loads) are available,
asymmetrical faults, which account for most faults, never result
in voltage sags to all single-phase loads (e.g, phase A-to-ground
faults may not cause voltage sags to the loads connectedbetween
phase B and neutral or phase C and neutral or loads connected
between phase B and phase C). Therefore, using
regardless of the number of phases involved, may not exactly
reflect the voltage sag performance of the distribution system.
From the demand sides, the indices are more interesting because
they can estimate the voltage sag performance for phase loads.

In order to take the availability of various phase loads in the
distribution system into account, this paper newly develops
in regard to phase loads as follows:
(10)
(11)
(12)
where
, , number of sags down to under
X% that phase-to-neutral
(A,B,C), phase-to-phase (A-B,
B-C, C-A), or three-phase load
experiences;
, , number of phase-to-neutral
(A,B,C), phase-to-phase (A-B,
B-C, C-A), or three-phase
customers served from the
system of interest.
TABLE I
S
YSTEM
FAUL T-RATE BREAKDOWN
Fig. 2. Mapping of the IEEE—123-bus radial distribution test feeder.
V. RESULT DEMONSTRATION AND ANALYSIS
A. Procedures of StochasticPrediction
The process of stochastic prediction study is performed
through the following steps.
First, the system fault rate (the total of faults occurring in the
test system over a certain period of time) is assumed to be an
arbitrary number, say 500 faults. This value is just for calcu-
lation and easier graphic demonstration of the results. Besides

that, contributory percentages of different fault types are also
assumed as follows:
•single phase to ground (N1): 80%;
• two phase to ground (N11): 10%;
• two phase together (N2): 8%;
• three phase to ground (N3): 2%
and the component fault rates are supposed to be
• transformer: 50%;
•line: 50%.
The listed percentages shown are, in
fact, based on actual survey
data
[9]. Based on the aforementioned assumptions, the system
fault rates of transformers and lines for different fault types due
to different fault causes (equipment failure or external causes)
are calculated and shown in columns 2 and 3 of Table I. Param-
eters (
, ) that are included make it possible to consider
the influence of fault causes due to external factors.
Second, the fault rate of each fault type is calculated for each
fault position using the fault distribution models as stated in
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KHANH et al.:FAULT DISTRIBUTION MODELING USING STOCHASTIC BIVARIATE MODELS 351
Fig. 3. Sag frequency spectrum and of different phase loads for the case the mean value is at node 13 and deviation .
Table I. The test system with actual dimensions in feet is mapped
out in Fig. 2. The fault positions are assigned with coordinates.
Third, the voltage sag magnitude and phase shift at all load

nodes are computed for all selected fault positions. With the ap-
plication of fault rates to the selected fault positions, the voltage
sag frequencies corresponding to different characteristics are
obtained. The voltage sag frequency is calculated for the fol-
lowing:
• individual load nodes;
• all possible phase loads, including phase-to-neutral,
phase-to-phase, and three-phase loads;
• the whole test system.
B. Evaluation
of Influences of the Fault Distributi
on Modeling
on the Voltage Sag Performance
The fault distribution modeling uses several parameters. In
practice, it is possible to adjust these parameters so that the re-
sulting model issuitable for the fault performance of the distri-
bution system of interest. However,the variation of these param-
eters also makes the voltage sag performance change accord-
ingly. In modeling fault distribution, this paper also considers
the following options of fault distribution for estimating the in-
fluences of fault distribution on voltage sag performance.
•
Change
contributory percentages of the fault due to ex-
ternal causes (change
or ). In this paper, three op-
tions
, 50%, and 100% are considered.
•Switch the position of the mean value (
, ) of the bi-

variate normal distribution. This paper considers four op-
tions of the mean value at nodes 13, 51, 67, and 85 as in-
dicated in Fig. 2.
• Vary the deviations
, of the bivariate normal distri-
bution. This paper also considers the options of the devi-
ation that are equal to 0.2, 0.5, and 0.8 of the maximum
value among deviations
.
C. Results Analysis
Based on aforementioned procedures of stochastic prediction,
the following are remarkable results.
In Fig. 3, the indices of voltage sag for different phase loads,
including voltage sag frequency spectrums, corresponding
, , and for X ranging
from 10% to 90% of the nominal voltage are shown. In this
case study,
, .
Besides that,
for the whole test system for dif-
ferent mean values (at nodes 13, 51, 67, and 85) of the fault
distribution models regardless of the number of involved
phases are also depicted in Fig. 4. Obviously, there are big
differences between
of different phase loads or
between
of phase loads and of the whole
system.
of phases A, B, and C are different
because the number of single-phase loads on each phase are

different.
are rather low as single-phase loads
just experience sags due to single-phase-to-ground faults on
the same phase. Generally,
are greater because
phase-to-phase loads are impacted by more faults (faults on
two phases) than phase-to-neutral loads (faults on one phase).
For phase-to-phase loads, there isalittle deep sag frequency;
meanwhile, the shallow sag frequency rises greatly because al-
most phase-to-ground faults (80% system fault rate) just cause
shallow sags to phase-to-phase loads.
for three
phases is the greatest and
for is equal
to 500 sags per load because three-phase loads will experience
voltage sag for any fault type. The aforementioned remarks
also explainwhy
, defined for phase loads, is for more
useful indices for estimating the voltage sag performance in the
distribution system where many single-phase loads exist.
Fig. 4 also shows that different positions of the mean value of
fault distribution models result indifferent spectrums of voltage
sag frequency. It is notable that if the position of mean value gets
closer to the bulk point of supply, the deep sag frequency will
increase, that is, mainly because of the radial network topology
of the distribution system.
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352 IEEE TRANSACTIONS ON POWERDELIVERY , VOL. 23, NO. 1, JANUARY 2008
Fig. 4. Sag frequency spectrum and of the whole system for different mean positions for the case that the deviation is .
Fig. 5. Voltage sag frequency spectrum of the load-bus 63 on phase A for dif-
ferent deviations. The mean value is at node 67 (upper) and node 13 (lower).
Fig. 6. Voltage sag frequency spectrum for loads on phase A for different de-
viations. The mean value is at node 67 (upper) and node 13 (lower).
Figs. 5 and 6 plot the voltage sag frequency for load node
63 (see Fig. 2) on phase A and for all loads on phase A for
Fig. 7. Voltage sag frequency spectrum and for the whole system for
different deviations for the mean value at node 67.
Fig. 8. Voltage sag frequency spectrum and for the whole system for
different deviations for a mean value at node 13.
different deviation values of fault distribution
in the case the mean values are identical to
the coordinates of node 13 and node 67. Similarly, Figs. 7 and 8
demonstrate the voltage sag frequency spectrum and
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KHANH et al.:FAULT DISTRIBUTION MODELING USING STOCHASTIC BIVARIATE MODELS 353
Fig. 9. Voltage sag frequency distribution for sags lower than 10%, 40% to 50%, 60% to 70%, and 70% to 80%, , , mean at
node 67.
for the whole test system also for different deviation values
and for the mean values at
node 13 and node 67. Increasing the deviation values
and
will turn the normal distribution into the uniform distribu-
tion. It causes shape variations to the voltage sag frequency
spectrum. The clear increase of the frequency of deep sags is

shown in all cases of the sag performance demonstration. If
the mean position of the distribution model is located at node
13, which is very near the bulk point, the frequency of sags
below 10% isevenraised by about 50% for the small deviation
. That is also explained as the result of
the radial network topology of the distribution system.
The spectrum of the voltage sag frequency for different case
studies (from Figs. 3–8) isquite similar inwhich deep sags ac-
count for a large number mainly due to short feeders in the dis-
tribution system. The frequency of 40% to 60% sags is also high
as the network topology consists of one trunk line with many lat-
eral taps in the middle. That means the point of common cou-
pling of many load nodes is on the middle of the trunk line.Few
load nodes connected to the trunk line near the bulk point of
supply (the distribution substation) explain why the shallow sag
frequency is very low.F
ig
. 9gives us a closer look at the voltage
sag frequency distribution for different sag magnitudes. It is,
without doubt, that deep sag frequencies appear at the nodes
on branches connected close to the far end of the trunk line.
Voltage sags 40% to 50% are distributed rather uniformly ex-
cepting nodes near the bulk point. The shallow sag frequencies
mainly occur at several nodes near the bulk point of supply.
VI. C
ONCLUSION
This paper presented a new method of fault distribution mod-
eling in the stochastic prediction of voltage sag for the distri-
bution system using 2-D distribution models. When using 2-D
distribution models for modeling fault distribution, parameters

of the distribution model should be selected properly to match
the monitored historical data of fault performance of the system
of interest. By using the bivariate normal distribution for mod-
eling fault distribution, this paper also analyzed the influences
of its
parameters on voltage sag performance. It i
s notable that
the alteration of the deviation value of the distribution has a
much stronger impact on sag performance, especially for the
deep sag frequencies pattern than switching the position of the
mean value. The more concentrated occurrence of faults on one
location in the distribution system of interest will increase the
number of deep sags. The results are also evidence that the typ-
ical radial network topology of the distribution system is also
another important reason for the high frequency of deep sags.
2-D stochastic models, such as the bivariate normal distribu-
tion used for modeling fault distribution, can provide a good
o
v
erview of fault performance of the whole system of interest.
Thus, it is possible not only to analyze the relation between
faults and voltage sags at individual locations of the system,
such as a specific load node or a segment of line, but also to
compute system indices of voltage sags, such as
.
The application of 2-D stochastic models has some limits to
the size of the system of interest.For the sections of the dis-
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354 IEEE TRANSACTIONS ON POWERDELIVERY , VOL. 23, NO. 1, JANUARY 2008
tribution system, of which the size is so large as the one sup-
plied from a bulk distribution substation, it is practical to use
this fault distribution modeling. The accuracy will be further
improved for the distribution systems, of which the topology
features the uniform arrangement of components. In addition,
the stochastic prediction of the transmission system should be
included if the influence of fault occurring in the transmission
system on voltage sag performance in the distribution system of
interest is considered.
The
presence
of different phase loads in the distribution
system indicated that
for the whole system without
considering the number of phase of the loads cannot reflect
voltage sag performance properly. To have a better assessment
of the voltage sag, this paper develops modified
regarding phase loads. The results proved that there are
bigdifferences between
, , and
for different phase loads and for the
whole system. This modification of
is more practical
from the customer’spoint of view when power-supply contracts
are set up.
R
EFERENCES
[1] R. C. Dugan, M.F.McGranaghan, and H. W. Beaty, ElectricPower

System Quality. New York: McGraw-Hill, 1996.
[2] M. H. J. Bollen, Understanding Power Quality Problems—Voltage
Sags and Interruptions. New York: IEEE Press, 2000.
[3] D. L. Brooks, R. C. Dugan, M. Waclawiak, and A. Sundaram, “Indices
for assessing utility distribution system RMS variation performance,”
IEEE Trans. Power Del.,vol. 13, no. 1, pp. 254–259,
Jan. 1998.
[4] M. R. Qader, M. H. J. Bollen, and R. N. Allan, “Stochastic prediction
of voltage sags in a large transmission system,” IEEE Trans. Ind. Appl.,
vol. 35, no. 1, pp. 152–162, Jan./Feb. 1999.
[5] J. V. Milanovic, M. T. Aung, and C. P. Gupta, “The influence of fault
distribution on stochastic prediction of voltage sags,” IEEE Trans.
Power Del.,vol. 20,
no. 1,
pp. 278–285, Jan. 2005.
[6] R.E.Brown, ElectricPower Distribution Reliability. New York:
Marcel-Dekker, 2002.
[7] IEEE Distribution Planning Working Group Report, “Radial distribu-
tion test feeder,” IEEE Trans. Power Syst.,vol. 6, no. 3, pp. 975–985,
Aug. 1991.
[8] W. H. Kersting,Distribution System Modeling and Analysis. Boca
Raton, FL: CRC, 2002.
[9]
T
. A. Short, ElectricPower Distribution Handbook. Boca Raton, FL:
CRC, 2004.
[10] G. Olguin, “Voltage dip (sag) estimation in power system based on sto-
chastic assessment and optimal monitoring,” Ph.D. dissertation, Dept.
Energy Environ.,Div.Elect. Power Eng., Chalmers Univ. Technol.,
Gotteborg, Sweden, 2005.

[11] M. R. Qader, M. H. J. Bollen, and R. N. Allan, “Stochastic prediction
of
voltage sags in reliability test system,” presented at the PQA-97 Eu-
rope, Elforsk, Stockholm, Sweden, Jun. 1997.
[12] J. A. Martinez-Velasco and J. Martin-Arnedo, “Stochastic prediction
of voltage dips using an electromagnetic transient program,” presented
at the 14th PSCC, Sevilla, Spain, Jun. 2002, Paper 4, Session 24.
Bach Quoc Khanh received the B.S. and Ph.D. de-
grees in power network and systems from Hanoi Uni-
versity of Technology, Hanoi,Vietnam, in 1994 and
2001, respectively. He received the M.S. degree in
system engineering from the Royal Melbourne Insti-
tute of Technology (RMIT), Melbourne, Australia, in
1997.
He is currently a Lecturer with the Faculty of
Electrical Engineering, Electric Power System
Department, Hanoi University of Technology. He
was a Postdoctoral Fellow with the Power System
Laboratory, School of Electrical Engineering and Computer Science, Seoul
Nat
ional University, Seoul, Korea. His special fields of interest include power
distribution system analysis, DSM, and power quality.
Dong-Jun Won (M’05) was born in Korea on Jan-
uary 1, 1975. He received the B.S.,M.S., and Ph.D.
degrees in electrical engineering from Seoul National
University,Seoul, Korea, in 1998, 2000, and 2004, re-
spectively.
Currently, he isaFull-Time Lecturer with the
School of Electrical Engineering with INHA Univer-
sity, Incheon, Korea. He was a Postdoctoral Fellow

with the Advanced Power Technologies Center,
Department of Electrical Engineering, University of
Washington, Seattle. His
research i
nterests include
power quality, dispersed generation, renewable energy, and hydrogen economy.
Seung-Il Moon (M’93) received the B.S. degree
in electrical engineering from Seoul National Uni-
versity, Seoul, Korea, in 1985 and the M.S. and
Ph.D. degrees in electrical engineering from The
Ohio State University, Columbus, in 1989 and 1993,
respectively.
Currently, he is an Associate Professor of the
School of Electrical Engineering and Computer
Science at Seoul National University. His special
fields of interest include power quality, flexible ac
transmission systems (FA
CTS), renewable energy,
and dispersed generation.
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
Abstract This paper presents a method of assessing a
power quality phenomena in distribution systems - voltage sag.
The voltage sag performance is obtained by the problem of
stochastic prediction of voltage sag in power systems [2] basing

on System Average RMS variation Frequency Index (SARFI
X
).
However, SARFI
X
is modified into SARFI
X-CURVE
that
considers not only the magnitude of voltage sag, but also its
duration. The resulting SARFI
X-CURVE
provides a better
understanding of the influence of voltage sag on the electric
loads. The duration of voltage sag is modeled regarding the
tripping time of protective devices in distribution systems. The
paper also applies this method to assess voltage sag
performance of the 22kV feeder 482-E14 of 110/35/22kV Giam
substation in Hanoi city, Vietnam.
Index Terms power quality, voltage sag, distribution
system, equipment compatibility curve, fault distribution
modeling, tripping time.
I. INTRODUCTION
MONG power quality phenomena, the voltage sag
(dip) is defined at IEEE1159, 1995 as a decrease in
RMS voltage to between 0.1 and 0.9 of the nominal voltage
at the power frequency for the duration of 0.5 cycle to 1
minute. Interests in the voltage sag have been getting much
greater recently due to its problems causing on the
performance of sensitive electronic equipments that are
widely used.

Researches about the voltage sag are usually related with
a basic process known as a “compatibility assessment” [1]
which includes three steps: i. Obtain the voltage sag
performance of the system of interest, ii. Obtain equipment
voltage tolerance, iii. Compare equipment voltage tolerance
with the voltage sag performance and estimate expected
impacts of the voltage sag on the equipment. Researches to
date have already evidenced that obtaining the voltage sag
performance is still needing much further improvement. The
information about the voltage sag is mainly obtained by
monitoring and stochastic prediction [1]. This paper
presents a method of predicting voltage sags in distribution
system using SARFI
X-CURVE
that is derived from SARFI
X
with regard to tripping time of protective devices currently
used in power distribution networks in Vietnam.

Bach Quoc Khanh is with Electric Power System Department,
Electricity Faculty, Hanoi University of Technology, 1 Dai Co Viet Rd.,
Hanoi, Vietnam (e-mail: ).
II. INDICES FOR VOLTAGE SAG ASSESSEMENT
Voltage sag assessment often bases on its characteristics:
magnitude and duration. There are many indices proposed
for voltage sag quantification [1], [2] and one of frequently
used indices is SARFI
X
that is defined as follows
N

N
SARFI
i
iX
X
¦

)(
(1)
where
X rms voltage threshold; possible values – 10-90%
nominal voltage
N
X(i)
Number of customers experiencing voltage sag with
magnitudes below X% due to measurement event i.
N number of customers served from the section of the
system to be assessed
Despite being widely used, SARFI
X
only considers the
magnitude of voltage sag and, of course, its value is maybe
much greater than the actual number of tripping electrical
appliances, especially when the duration of sags is small
enough (less than a half second). To take the sag duration
into account, SARFI
X
is developed into SARFI
X-CURVE
[2],

[4], [6] which is defined below
Figure 1. ITI curve for susceptibility of computer equipment.
Prediction of Voltage Sags in Distribution
Systems With Regard to Tripping Time of
Protective Devices
Bach Quoc Khanh (Hanoi University of Technology)
A
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N
N
SARFI
m
i
iX
CURVEX
¦



1
'
)(
(2)
where
'

)(iX
N
:Number of customers tripped when experiencing
voltage sag with magnitudes below X% due to measurement
event i.
SARFI
X-CURVE
corresponds to voltage sags below an
equipment compatibility curve. So far, frequently used
curves are CBEMA, ITIC and SEMI [1]. Obviously,
SARFI
X-CURVE
can provide a better understanding of the
influence of voltage sag on the operation of electric
equipment in electric networks. This paper presents the
method of calculating SARFI
X-CURVE
using ITI curve (Figure
1) as a case study.
III.
REDICTION OF VOLTAGE SAG IN DISTRIBUTION SYSTEM
A. Problem definition
The problem of stochastic prediction of voltage sag can
obtain the voltage sag performance of a specific electric
system by using data of events leading to sags. In fact, more
than 90% sag events are resulted from short-circuits and it is
possible to use fault modeling and short-circuit calculation
tools to predict voltage sags in the power system (Figure 2).
This work uses the method of “fault position” [1] for
voltage sag prediction in distribution systems with following

significant steps
- Modeling the fault distribution on of a given
segment of distribution system (see part B)
- Calculating the short-circuit current and voltage
sags at all influenced load nodes.
- Cumulating system voltage sags with different
characteristics and obtaining SARFI
X
.
- Cumulating system voltage sags that cause
equipment to trip and obtaining SARFI
X-CURVE
.
To obtain SARFI
X-CURVE
, this work uses the typical
tripping curve (t
PD
= f(I
F
)) of protective devices like fuses,
feeder circuit breakers currently used in distribution
systems. Each sag is plotted as a point characterized by a
pair of co-ordinates (magnitude of voltage sag and tripping
time). If the point falls out of voltage tolerant envelop
(Figure 1), the sag is cumulated to calculate SARFI
X-CURVE
.
B. Fault Distribution Modeling
Modeling the fault distribution is to determine the short-

circuit fault frequency (i.e. fault rate or the number of short-
circuit faults per year) for all fault types at all possible fault
positions throughout the system of interest [3]. It consists of
the selection of fault position and fault type and the
distribution of fault rate for selected fault positions and fault
types.
Fault positions are generally chosen in the way that a
fault position should represent short-circuit faults leading to
sags with the similar characteristics [1]. For the distribution
system with typically radial network topology, small line
segments and distribution transformers along the trunk
feeders, it is possible to apply only one fault position for
each distribution transformer and also one fault position for
each line segment.
Different fault types should be applied to each fault
position mainly depending on number of phases available at
the selected fault positions. The fault rate of each fault type
is normally referred from the observed historical data.
Fault rate mainly depends on fault position, fault type
and fault cause. For a segment of distribution system that is
geographically seen as small area, it possible to assume that
fault rate of each fault type follows uniform distribution for
all fault positions. [3]. In this sense, the fault rate at each
position is identical to component failure rate that is based
on component reliability. In reality, uniform fault
distribution is a practical assumption for distribution
systems because the service area of a certain distribution
line outgoing from a distribution substation is normally
small.
C. Assumptions

Besides fault distribution modeling, for the distribution
system, following assumptions are possibly considered [3].
- Voltage sags are only caused by faults in the
distribution system.
- If the distribution system is supposedly a section of a
large distribution system, only faults occurred within it are
considered. The faults in sections fed from other distribution
substations can be skipped as the transformer impedance in
distribution substations, in reality, is rather high. Similarly,
the faults in low voltage networks are also ignored because
of the large impedance of distribution transformers. This
assumption only neglects voltage sags caused by faults in
the transmission system. It will be considered if the
stochastic prediction of voltage sag in large transmission
systems [7] is included.
- In terms of reliability, the distribution system is
modeled on two main components: lines and distribution
transformers. The reliability of any other distribution
equipment is supposedly included in the reliability of these
two components.
- The fault positions are selected as mentioned in the Part
III.B. For transformers, one fault position each load node
(i.e. the nodes connected with distribution transformers) is
applied. For lines, one fault position is also applied for each
line segment. Because of short line segments, the paper
selects the fault position at the end of each line segment.
- Fault types (single phase to ground, phase to phase, two
phases to ground and three phases to ground) are applied to
fault positions depending on the number of available phases.
~

Z
S
Z
F
V
t
E
L
oad at PC
C
Short circuit
Figure 2. Model of voltage sag
prediction in power systems
t
PD
V
Sag
E
t
V
t
t
PD
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The fault impedance is assumed to be negligible.

D. System voltage sag calculations
Short-circuit calculations and resulting voltage sag
magnitude at load nodes in distribution systems is
performed by MatLab programming that used in [3]. The
program consists of two modules
- Short circuit calculation
- Fault distribution modeling
Its block diagram is briefly depicted as Figure 3

IV. A C
ASE STUDY
A. Case study definition
This work illustrates the method by predicting voltage
sag performance and resulting SARFI
X-CURVE
for a 24kV
feeder network in Hanoi, Vietnam. Preliminary data is as
follows
The network segment under consideration: Feeder 482-
E14, 24kV, underground cable, outgoing from 110/35/22kV
Giam substation. It’s a radial network with 99 nodes and 98
branches. Fault positions can be selected at load nodes for
distribution transformer fault and at all nodes for line fault.
Besides, contributory percentages of different fault type
are also assumed as follows
- Single phase to ground (N1) : 65%
- Two phase to ground (N11) : 10%
- Two phase together (N2) : 20%
- Three phase to ground (N3) : 5%
and the component fault rates are supposed to be

- Transformer : 50%
- Line : 50%
The tripping curve used for this work is the typical
inverse curve of in-service protective devices in distribution
systems like fuse-cutout for distribution transformer
protection, overcurrent relay for 24kV line feeder. The
common formula of tripping curve is
1)(
*


b
PD
I
a
t
(3)
where
I*: Ratio of fault current I
N
and pickup current I
P
.
a, b: Constants that are selectable.
V. R
ESULT DEMONSTRATION AND ANALYSIS
Firstly, the system fault rate (the total of faults occurring
in the test system over a certain period of time) is assumed
to be an arbitrary number, say, 100 faults. This value is just
for calculation and easier graphic demonstration of the

results. The system fault rate is then distributed uniformly to
all fault positions as assuming in Part III.B. Short-circuit
calculation is made at every fault positions and resulting
voltage sags at all load nodes are identified by their
magnitudes. Besides, the fault current is used to determine
voltage sag duration as per (3) and each voltage sag
identified above are again checked to see whether it is to fall
inside the voltage tolerant envelope of ITI curve or not. If it
is inside, it is taken into account for calculating SARFI
X-
CURVE
. Finally two indices SARFI
X
and SARFI
X-CURVE
are
obtained and plotted in the same graphics for analysis. The
results are depicted on two graphics. Figure 5 depicts the
system voltage sag frequency spectrum. Figure 6 depicts
SARFI
X
and SARRFI
X-CURVE
.
The results also indicate some following remarks
- Deep sag frequency rises highly due to the radial
network topology with short distances of cable
lines in distribution systems.
- 40-50% sag is also a little greater than other sags
because the feeder consists of one trunk line with

many lateral taps in the middle. That means the
Figure 3. Block-diagram of voltage sag prediction
and SARFI
X-CURVE
in distribution systems
START
DETERMINE FAULT LINE
Find nodes and branches on
fault current carrying line
STOP
ON FAULT-LINE CALCULATION
Calculate fault current I
N
and
sags V
S
at nodes on fault line
SARFI
X
CALCULATION
Sag quantification by magnitude
calculation
O
FF FAULT-LINE CALCULATION
Calculate voltage sags V
S
at
nodes not on fault line
SARFI
X-CURVE

CALCULATION
Sag quantification by duration
TRIPPING TIME
t
PD
=
f
(
I
N
)
24kV bus of
110kV Giam
substation
Circuit
b
reake
r
Fuse
Fuse
Distribution
transforme
r
Distribution
transforme
r
Figure 4. Brief description of
24kV feeder protection system
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point of common coupling of many load nodes is
on the middle of the trunk line.
- Voltage sags with X greater than 70% are very few
because the system and distribution transformer
impedances normally are much higher than
distribution lines.
- SARFI
X
and SARFI
X-CURVE
are slightly different
because the tripping time of protective devices in
distribution systems is typically 0.5 seconds and
frequencies of voltage sag of 70-80% and 80-90%
are very small. In ITI curve, sags with the
magnitude X lower than 70% nominal voltage
feature very short duration (less than one cycle)
and thus they are certainly taken in to account for
calculating SARFI
X-CURVE
.
VI. C
ONCLUSIONS
This paper presented a method of assessing voltage sags
in distribution systems with regard to tripping time of
protective devices. The assessment bases on SARFI

X-CURVE
that combines SARFI
X
and equipment compatibility curves.
Therefore, the results of assessment provide a better
understanding of the influence of voltage sag on loads.
This method is also found useful for power quality
assessment and power supply contracting principles for
power distribution utilities in Vietnam in the process of
electricity market establishment because the management of
distribution system is becoming financially separated from
the power system.
The application of the method has some limits that can be
developed in further researches. For a larger network, a
more suitable fault distribution should be considered [3],
[5]. In addition, a combination of the problems of predicting
voltage sags in distribution systems and transmission system
[7] will provide a more comprehensive understanding of
voltage sag performance of a power system.
VII. R
EFERENCES
[1] M.H.J. Bollen, Understanding power quality problems - voltage sags
and interruptions, IEEE Press, 2000.
[2] Recommended practice for the establishment of voltage sag indices,
Draft 6, IEEE P1564, Jan 2004.
[3] Bach Quoc Khanh, Dong Jun Won, Seung Il Moon, “Fault
Distribution Modeling Using Stochastic Bivariate Models For
Prediction of Voltage Sag in Distribution Systems”, IEEE Trans.
Power Delivery, pp. 347-354, Vol.23, No.1, January 2008.
[4] Juan A. Martinez, Jacinto Martin-Arnedo, “Voltage Sag Studies in

Distribution Networks - Part II: Voltage Sag Assessment, Part III -
Voltage Sag Index Calculation”, IEEE Trans. Power Delivery, pp.
1679-1697, Vol. 21, No. 3, July 2006.
[5] Jovica V. Milanovic, Myo Thu Aung, C. P. Gupta, “The Influence of
Fault Distribution on Stochastic Prediction of Voltage Sags”, IEEE
Trans. Power Delivery, pp. 278-285, Vol. 20, No. 1, Jan 2005.
[6] D. L. Brooks, R. C. Dugan, Marek Waclawiak, Ashok Sundaram,
“Indices for Assessing Utility Distribution System RMS Variation
Performance”, IEEE Trans. Power Delivery, vol.13, no.1, pp.254-259,
Jan. 1998.
[7] M.R.Qader, M.H.J.Bollen, and R.N.Allan, “Stochastic Prediction of
Voltage Sags in a Large Transmission System”, IEEE Trans. Industry
Applications, vol.35, no.1, pp.152-162, Jan./Feb. 1999.
[8] M.R.Qader, M.H.J. Bollen and R.N.Allan, “Stochastic Prediction of
Voltage Sags in Reliability Test System”, PQA-97 Europe, Elforsk,
Stockholm, Sweden, Jun. 1997.
VIII. BIOGRAPHIES
Bach Quoc Khanh received B.S. and Ph.D. degrees in power network
and systems from Hanoi University of Technology, Hanoi, Vietnam in 1994
and 2001 respectively. He received M.S. in system
engineering from RMIT, Melbourne, Australia in
1997. He is a teaching staff of Electric Power
System dept., Electrical Engineering Faculty,
Hanoi Univeristy of Technology. His special
fields of interest include power distribution
system analysis, DSM and power quality.
0
5
10
15

20
25
30
35
40
45
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
Sag
Sag leading load failure
System voltage sag frequency
V
Sag
(percentage of U
n
)
Figure 5. System voltage sag frequency spectrum
0
20
40
60
80
100
120
<10<20<30<40<50<60<70<80<90
SARFI
SARFI
X
SARFI
X-CURVE
V

Sag
(percentage of U
n
)
Figure 6. SARFI
X
and SARFI
X-CURVE
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TẠP CHÍ KHOA HỌC & CÔNG NGHỆ CÁC TRƯỜNG ĐẠI HỌC KỸ THUẬT 

SỐ 77 - 2010
72

ĐÁNH GIÁ SỤT GIẢM ĐIỆN ÁP NGẮN HẠN
TRÊN LƯỚI TRUYỀN TẢI ĐIỆN 220KV VIỆT NAM
PREDICTION OF VOLTAGE SAGS IN THE 220KV TRANSMISSION SYSTEM OF VIETNAM

Bạch Quốc Khánh
Trường Đại học Bách Khoa Hà Nội
Phùng Thế Anh
Công ty CP Tư vấn Xây dựng Điện I

TÓM TẮT
Bài báo trình bày phương pháp đánh giá một hiện tượng chất lượng điện năng (CLĐN) trên lưới
truyền tải điện (LTT) là sụt áp ngắn hạn (SANH - voltage sag) [1]. Mô hình đánh giá SANH dựa trên

phương pháp dự báo ngẫu nhiên SANH [2] trong hệ thống điện (HTĐ). Việc đánh giá này dựa trên chỉ
tiêu tần suất SANH trung bình của HTĐ với đặc tính X (SARFI
X
) và SARFI
X-CURVE
[3] cho phép xét đến
không chỉ đặc trưng biên độ của SANH mà còn cả đặc trưng thời gian tồn tại SANH. Đối tượng tính
toán là hệ thống truyền tải điện 220kV của Việt Nam theo tổng sơ đồ 6 với tỷ lệ suất sự cố ngắn mạch
thực tế của năm 2008. Việc đánh giá này là một cố gắng đầu tiên định lượng hóa tình hình một hiện
tượng chất lượng điện năng phổ biến trên một lưới điện diện rộng thực tế giúp cho việc đánh giá chất
lượng điện năng nói chung của hệ thống điện Việt Nam hiện nay.
ABSTRACT
This paper presents a method of predicting a power quality phenomena in distribution systems,
voltage sag [1]. The calculation of voltage sag performance follows the model of stochastic prediction
of voltage sag in power systems [2]. The voltage sag performance is predicted basing on the System
Average RMS variation Frequency Index (SARFI
X
) and SARFI
X-CURVE
[3] that considers not only the
characteristics - magnitude, but also the characteristics – duration of voltage sag. The objective of
research is the whole 220kV transmisson systems in Vietnam as per the 6
th
master-plan with actual
data of fault rate of the year 2008. This prediction is the first effort of quantifying the voltage sag
performance for such a large transmission system that helps assess the power quality of the electric
power system in Vietnam now.

I. ĐẶT VẤN ĐỀ
Theo IEEE-1159, 1995, SANH (voltage

sag) là hiện tượng CLĐN trong đó giá trị điện
áp hiệu dụng của lưới điện sụt giảm còn từ 0,1
đến 0,9 điện áp định mức trong thời gian từ 0,5
chu kỳ đến 1 phút [1]. SANH có thể làm cho
các thiết bị điện nhậy cảm như điện tử công
suất, các bộ điều tốc hay máy tính cá nhân
ngừng hoặc làm việc không mong muốn. Hiện
tượng này
lại rất hay
xảy ra, trong khi để nâng
cao hiệu suất quá trình hay việc ứng dụng các
công nghệ mới, các thiết bị điện ứng dụng điện
tử công suất ngày càng được sử dụng nhiều, do
đó SANH ngày càng được quan tâm nghiên
cứu. Trước khi xem xét những giải pháp khắc
phục tác động của SANH, yêu cầu đánh giá
SANH trong HTĐ luôn được đặt ra. Quá trình
đánh giá CLĐN nói chung và SANH nói riêng
thường trải qua ba khâu chủ yếu [1] là i. Nhận
dạng tình hình CLĐN được cung cấp, ii. Xác
định yêu cầu CLĐN của các phụ tải, iii. So
sánh yêu cầu CLĐN của phụ tải với tình hình
CLĐN được cung cấp và
đánh giá tác đ
ộng của
CLĐN đối với phụ tải. Việc xác định yêu cầu
CLĐN của các phụ tải thuộc về các nhà sản
xuất thiết bị dùng điện mà điển hình là đặc tính
chịu điện áp của phụ tải CBEMA, ITIC hoặc
SEMI [1] (Hình 1).

Trong khi đó, việc nhận dạng tình hình
CLĐN là nhiệm vụ của phía cung cấp điện.
Ở Việt Nam, đã bắt đầu có những nghiên
cứu chuyên sâu về đánh giá tình hình SANH
trong HTĐ [2, 3], tuy nhiên việc định lượng hóa
tình hình SANH trên HTĐ thực tế ở Việt Nam
vẫn chưa được thực hiện. Nguyên nhân chính
hiện nay
là k
hông có một cơ sở dữ liệu về
CLĐN nói chung và SANH nói riêng của HTĐ
Việt Nam do hệ thống giám sát và lưu trữ thông
tin về CLĐN vẫn còn rất thiếu. Bên cạnh việc
giám sát CLĐN, một cách gián tiếp để xác định
tình hình SANH trên HTĐ có thể dùng mô hình
dự báo CLĐN dựa trên các nguyên nhân sinh ra
nó. Trong các nguyên nhân này, trên 90%
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SANH là do sự cố ngắn mạch trong HTĐ. Do
đó, có thể đánh giá SANH thông qua mô phỏng
và tính toán ngắn mạch trên HTĐ theo phương
pháp điểm sự cố [1, 2].

Hình 1. Đường cong chịu điện áp của nhóm
thiết bị SEMI (Semiconduactor Equipment and
Materials International group)
Bài báo trình bày phương pháp dự báo
SANH trên toàn bộ lưới điện truyền tải 220kV
của HTĐ Việt Nam theo Tổng sơ đồ VI dùng
phương pháp điểm sự cố với số liệu sự cố ngắn
mạch trên lưới truyền tải 220kV thực tế của
năm 2008 và sử dụng chỉ tiêu SARFI
X
và
SARFI
X-CURVE
[3,4,8].
II. XÂY DỰNG MÔ HÌNH BÀI TOÁN
2.1 Phương pháp điểm sự cố dùng cho dự
báo SANH trong lưới điện truyền tải 220kV
Theo phương pháp này, giả thiết SANH
gây ra là do ngắn mạch trong HTĐ. Khi đó, đặc

trưng biên độ của SANH (Hình 2) được xác
định bởi vị trí và loại sự cố ngắn mạch [1, 4].
Đặc trưng thời gian tồn tại SANH thì phụ thuộc
vào thời gian loại trừ ngắn mạch của các thiết bị
bảo vệ.
Các đặc trưng trên đây của SANH được
xác định tại các nút phụ tải của lưới truyền tải
220kV là các trạm biến áp 220kV để từ đó xác
định các chỉ tiêu SARFI
X
và SARFI
X-CURVE
cho
cả hệ thống truyền tải điện 220kV của Việt
Nam.









Hình 2. Các đặc trưng của SANH
2.2. Xây dựng mô hình điểm sự cố đối với
lưới điện truyền tải 220kV của Việt Nam
- Chọn vị trí sự cố : Chỉ xét sự cố ngắn mạch
trên lưới 220kV. Các ngắn mạch xảy ra ở lưới
có điện áp thấp hơn có thể giả thiết là ít ảnh

hưởng đến lưới 220kV do tổng trở các máy biến
áp khu vực và địa phương là khá lớn. Vì bản
thân lưới 220kV đã rất lớn nên trong nghiên
cứu này chưa xét các sự cố ngắn mạch trên lưới
500kV và tại các nguồn điện. Biên độ SANH
tại các nút phụ tải phụ thuộc vào vị trí điểm
ngắn mạch. Về nguyên tắc sự cố có thể xảy ra
tại bất cứ đâu trên lưới 220kV, tuy nhiên nếu
trong một phạm vi của lưới điện mà ngắn mạch
ở đó đều dẫn đến SANH tại các nút phụ tải có
cùng đặc trưng biên độ thì chỉ cần chọn một vị
trí điển hình. Sơ đồ hệ thống truyền tải điện
220kV theo tổng sơ đồ VI [9] tính đến năm
2008 gồm 66 trạm 220kV, 98 nhánh đường dây
220kV với tổng chiều dài là 7988km. Sự cố
ngắn mạch trên lưới điện truyền tải được xét
cho cả đường dây và trạm biến áp nên đối với
sự cố trạm biến áp xét ở tất cả 66 nút có trạm
220kV, còn sự cố trên đường dây, tùy theo tổng
chiều dài mỗi nhánh đường dây mà xét một
hoặc vài điểm sự cố trên nhánh đó. Nhìn chung,
các điểm sự cố cách nhau từ 10km đến 40km.
Tổng số điểm ngắn mạch trên đường dây là 169
điểm.
- Chọn loại sự cố ngắn mạch : Lưới điện cao áp
là 3 pha, vai trò các pha như nhau nên khi xét
các dạng ngắn mạch thì xét 4 dạng với tỷ lệ
phân bố suất sự cố [10] :
Ngắn mạch 1 pha - đất : 65%
Ngắn mạch 2 pha : 20%

Ngắn mạch 2 pha - đất : 10%
Ngắn mạch 3 pha : 5%
Vùng mất an toàn
Vùng mất
an toàn
Vùng
an toàn
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- Phân bố sự cố ngắn mạch : Sự cố ngắn mạch
mang tính ngẫu nhiên phụ thuộc vào nhiều yếu
tố [2] nên suất sự cố nhìn chung khác nhau đối
với từng loại sự cố và vị trí sự cố. Trong nghiên
cứu này, do số liệu thống kê về phân bố sự cố
trên lưới truyền tải 220kV chưa đủ chi tiết nên
sự phân bố sự cố được đề xuất theo mô hình
phân bố đều. Theo thống kê của tổng công ty
truyền tải điện quốc gia lưới truyền tải 220kV
trong năm 2008 có tổng số 45 sự cố xảy ra tại
các nút trạm 220kV và 143 sự cố trên các
đường dây 220kV. Suất sự cố đường dây là
0,0179 sự cố/km/năm và của trạm biến áp là
0,682 sự cố/trạm/năm. Phân bố sự cố cho từng

loại ngắn mạch đối với đường dây và máy biến
áp được cho ở Bảng 1.
Bảng 1. Phân bố sự cố theo loại sự cố
Loại
Suất sự cố
Đường dây
Trạm biến áp
N
(1)

92,95
29,25
N
(1,1)

28,60
9,00
N
(2)

14,30
4,50
N
(3)

7,15
2,25
- Chọn vị trí nút phụ tải cần xác định SANH :
Trên lưới truyền tải, nút phụ tải là các nút có
trạm 220kV cấp điện xuống các lưới có điện áp

thấp hơn. Lưới 220kV lại có dạng mạch vòng
nên nhìn chung trên mỗi nhánh đường dây
220kV, bảo vệ được đặt tại cả hai đầu và khi
xảy ra sự cố ngắn mạch trên nhánh đường dây
nào thì nhánh đó sẽ bị cô lập riêng. Do đó, tất
cả các nút (66 trạm 220kV) trên lưới điện đều
bị SANH khi sự cố, không có nút nào bị mất
điện duy trì và ta phải tính SANH cho 66 nút
này.
2.3 Tính toán ngắn mạch và xác định đặc
trung biên độ SANH trong lưới điện truyền
tải 220kV của Việt Nam
Việc tính ngắn mạch và SANH tại các
nút phụ tải trong lưới truyền tải 220kV được
thực hiện bằng chương trình PSS/E. Sơ đồ khối
các bước tính toán như hình 3.
- Xác định SARFI
X
: Việc chọn vị trí và xác
định suất sự cố cho từng vị trí và từng loại sự
cố được thực hiện như ở 2.2. Dùng chương
trình PSS/E tính ngắn mạch tại từng điểm sự cố
với từng loại sự cố và từ đó xác định biên độ
SANH tại tất cả 66 nút phụ tải do từng điểm và
từng loại sự cố ngắn mạch gây ra. Gán suất sự
cố cho từng vị trí và từng loại sự cố sẽ rút ra
được tần suất SANH tại từng nút phụ tải do sự
cố đang xét gây ra. Lặp lại việc tính ngắn mạch
và SANH với các điểm sự cố khác rồi tổng hợp
lại ta được tần suất SANH với các đặc tính biên

độ khác nhau do sự cố tại tất cả các điểm ngắn
mạch trên lưới truyền tải 220kV gây ra, và cuối
cùng ta rút ra được chỉ tiêu SARFI
X
của toàn hệ
thống.
















Hình 3. Sơ đồ khối đánh giá SANH trên lưới
truyền tải điện 220kV Việt Nam
- Xác định SARFI
X-CURVE
: Để xác định SARFI
X-
CURVE
, phải xét đến thời gian loại trừ sự cố của

hệ thống bảo vệ lưới 220kV và dạng đặc tính
chịu điện áp lựa chọn. Đối với lưới 220kV của
Việt Nam hiện nay, bảo vệ chính là bảo vệ cắt
nhanh (so lệch dòng điện hoặc tổng trở cực
tiểu) với tổng thời gian cắt ngắn mạch từ 120ms
đến 150ms. Trong nghiên cứu sử dụng đặc tính
chịu điện áp của các phụ tải nhậy cảm là SEMI,
và với thời gian loại trừ sự cố như trên, các
SANH có biên độ dưới 70% đều rơi vào vùng
mất an toàn và làm các phụ tải nhậy cảm ngừng
làm việc. Do đó, khi xác định SARFI
X-CURVE
,
với X từ 70% đến 100% điện áp định mức thì
SARFI
X-CURVE
không đổi.
Mô phỏng phân bố sự cố trên
lưới truyền tải 220kV
Mô phỏng lưới điện, tính
ngắn mạch bằng PSS/E
Start
Tính SANH cho từng nút tải
bằng PSS/E
Tính SARFI
X
cho lưới truyền
tải điện 220kV
Tính SARFI
X-CURVE

cho
truyền tải điện 220kV
Stop
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III. PHÂN TÍCH KẾT QUẢ
Thực hiện trình tự tính toán như sơ đồ
khối ở hình 3, sau đây là tóm tắt một số kết quả
đáng lưu ý :
- Tần suất SANH trung bình của một nút phụ tải
bất kỳ :
Hình 4 và 5 biểu diễn kết quả tính toán
tần suất SANH tại nút trạm 220kV Mai Động,
Thành phố Hà Nội.







Hình 4. Tần suất SANH nút 220kV Mai Động
theo từng khoảng đặc trưng biên độ

Hình 5. Tần suất SANH nút 220kV Mai Động
theo đặc trưng biên độ lũy tiến





Hình 6. Tần suất trung bình SANH theo từng
khoảng đặc trưng biên độ SANH

Hình 7. SARFI
X
và SARFI
X-CURVE
của lưới
truyền tải điện 220kV tính cho năm 2008
Hình 4 biểu diễn tần suất SANH theo
từng khoảng đặc trưng biên độ của SANH.
Hình 5 biểu diễn tần suất SANH khi SANH có
biên độ nhỏ hơn từng mức đặc trưng biên độ.
- Tần suất SANH trung bình hệ thống :
Đối với mỗi phụ tải, tần suất SANH
trung bình theo từng khoảng đặc trưng biên độ
SANH được cho ở Hình 6. Và cuối cùng là chỉ
tiêu SARFI
X
của toàn bộ lưới truyền tải điện
220kV Việt Nam được cho ở Hình 7.
Từ kết quả cho ta một số nhận xét đáng
chú ý sau :
- Tần suất SANH ứng với từng loại sự cố tương
ứng với tần suất của từng loại sự cố.
- SANH nông (70%-90%) có tần suất khá lớn
và tần suất SANH dù của nút cụ thể là 220kV
Mai Động hay trung bình cho từng nút chỉ
khoảng 25 lần/năm rất nhỏ so với tổng số sự cố
trên lưới 220kV là 188. Đó là vì lưới 220kV trải
toàn quốc nên ngắn mạch xảy ra ở từng miền ít
ảnh hưởng đến các phụ tải tại các miền khác.
- Tần suất SANH ở nút 220kV Mai Động lớn

hơn SARFI
X
của toàn hệ thống vì lưới 220kV ở
miền Bắc có nhiều phụ tải hơn do địa bàn rộng
hơn.


N
(3)

N
(1,1)

N
(2)

N
(1)

Tần suất SANH
X
Tần suất SANH
X
SARFI
X

SARFI
X-CURVE

X

X
Tần suất
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V. KẾT LUẬN
Bài báo đã trình bày phương pháp đánh
giá SANH trên lưới truyền tải điện 220kV của
Việt Nam thông qua chỉ tiêu SARFI
X
và
SARFI
X-CURVE
. Đây là cố gắng đầu tiên để định
lượng hóa việc đánh giá tình hình SANH nói
riêng và CLĐN nói chung trong HTĐ Việt Nam
trên một diện rộng.
Nghiên cứu trong bài báo cũng cần được
phát triển thêm. Kết quả đánh giá SANH trong
lưới truyền tải điện cần được xét thêm các
SANH do ngắn mạch ở phần nguồn và lưới
truyền tải điện 500kV. Hơn nữa, nghiên cứu
cũng còn có thể phát triển việc xem xét các yếu
tố ảnh hưởng đến phân bố sự cố khi lưới truyền

tải điện của Việt Nam trải trên một phạm vi
rộng lớn với tình hình sự cố khác nhau. Các mô
hình ngẫu nhiên với các luật phân bố xác suất
phù hợp với tình hình xảy ra sự cố thực tế có
thể được xem xét [2, 6, 8].
TÀI LIỆU THAM KHẢO
1. M. H. J. Bollen; Understanding power quality problems - voltage sags and interruptions; IEEE
Press, 2000.
2. Bach Quoc Khanh, Dong Jun Won, Seung Il Moon; Fault Distribution Modeling Using Stochastic
Bivariate Models For Prediction of Voltage Sag in Distribution Systems; IEEE Trans. Power
Delivery, Vol.23, No.1, pp.347-354, Jan. 2008.
3. Bach Quoc Khanh; Prediction of Voltage Sags in Distribution Systems With Regard to Tripping
Time of Protective Devices; Proceeding, EEE.CR.ASPES2009, Tech. Section 2.1., Hua Hin,
Thailand, Sep. 28-29, 2009.
4. D. L. Brooks, R. C. Dugan, Marek Waclawiak, Ashok Sundaram; “Indices for Assessing Utility
Distribution System RMS Variation Performance”; IEEE Trans. Power Delivery, Vol.13, No.1,
pp.254-259, Jan. 1998.
5. M.R.Qader, M.H.J.Bollen, and R.N.Allan; “Stochastic Prediction of Voltage Sags in a Large
Transmission System”; IEEE Trans. Industry Applications, Vol.35, No.1, pp.152-162, Jan./Feb.
1999.
6. Juan a. marTíNez-Velasco; “Computer-Based Voltage Dip Assessment in Transmission and
Distribution Networks”, Electrical Power Quality and Utilisation, Journal Vol.XIV, No.1, 2008.
7. J.V.Milanovic, M.T.Aung and C.P.Gupta; “The Influence of Fault Distribution on Stochastic
Prediction of Voltage Sags”; IEEE Trans. Power Delivery, vol.20, no.1, pp.278-285, Jan. 2005.
8. Recommended practice for the establishment of voltage sag indices, Draft 6, IEEE P1564,
Jan
2004.
9. Tổng sơ đồ phát triển Hệ thống điện Việt Nam, Bản IV, Viện Năng lượng, 2006.
10. T. A. Short; Electric Power Distribution Handbook, CRC Press, 2004.

Địa chỉ liên hệ : Bạch Quốc Khánh - Tel: 0904.698.900, email:
Bộ môn Hệ thống điện, Khoa Điện, Trường Đại học Bách khoa Hà Nội
Số 1, Đại Cồ Việt, Hà Nội

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
Abstract— In this paper, a novel effort for prediction of
voltage sag in the entire transmission system of Vietnam is
presented. As the Vietnamese electricity industry moves toward
the electricity market, prediction will help utilities have early
assessment of power quality in transmission system. The
proposed prediction approach uses a fault position method in
which the fault distribution in the transmission system is created
based on an actual fault occurrence in the entire 220kV and
500kV transmission system throughout Vietnam that took place
in 2008. The research also makes use of the SARFI
CURVE
with
ITIC and SEMI curve, which takes into account of the actual
fault clearing time of protective devices used in transmission
system in Vietnam. By using SARFI
CURVE
, a better assessment of
voltage sag performance is obtained in the transmission system
with regard to load’s voltage tolerance.

Index Terms transmission system, power quality, voltage sag

frequency, stochastic prediction, fault distribution, fault clearing
time, ITIC, SEMI curve.
I. INTRODUCTION
mong power quality phenomena, voltage sag (dip) is
defined by IEEE 1159 (1995) as a decrease in RMS
voltage to between 0.1 to 0.9 of nominal voltage at power
frequency for duration of 0.5 cycle to 1 minute. Interests in
voltage sag has been getting much greater recently in Vietnam
due to its impact on the performance of sensitive electronic
equipment like variable speed drives, computer-controlled
production lines that are widely used, especially in industry.
Although voltage sags are more common in distribution
system, many causes leading to voltage sag are derived from
transmission systems. An assessment of voltage sag in
transmission systems is important for utilities and customers
in Vietnam now.
Voltage sag assessment normally comes prior looking for
the solution of voltage sag mitigation. Voltage sag assessment
is usually related with the basic process known as a
“compatibility assessment” [1] which includes three steps: (i).
Obtain the voltage sag performance of the system of interest,
(ii). Obtain equipment voltage tolerance and (iii). Compare
equipment voltage tolerance with the voltage sag performance


Bach Quoc Khanh is a faculty member with Electric Power Systems
Department, Electrical Engineering Faculty, Hanoi University of Science and
Technology, 1 Dai Co Viet Rd., Hanoi, Vietnam (e-mail: bq_khanh-
).
Nguyen Hong Phuc is a master student with Electric Power System

Department, Electricity Faculty, Hanoi University of Science and Technology,
1 Dai Co Viet Rd., Hanoi, Vietnam (e-mail: ).
and estimate expected impact of voltage sag on the equipment.
The permissible voltage tolerance for electric equipment,
normally defined by the manufacturers and the well-known
PQ curves for susceptibility of computer equipment displays
are CBEMA, ITIC or SEMI [1] whereas power quality
assessment of power supply system is utilities duty. This paper
is the first effort to assess the voltage sag performance in the
transmission system of Vietnam by using the method of
stochastic prediction of voltage sags [1], [2], [3] using
SARFI
CURVE-X
that is derived from SARFI
X
with regard to
fault clearing time of protective devices currently used in the
transmission system in Vietnam.
II. I
NDICES FOR VOLTAGE SAG ASSESSMENT
Voltage sag assessment often relies on voltage sag
characteristics: magnitude and duration. There are many
indices proposed for voltage sag quantification. [1], [4] In this
paper the authors use one of the frequently used indices,
SARFI
X
. It is defined as follows
N
N
SARFI

i
iX
X


)(
(1)
where
X rms voltage threshold; possible values – 10-90% nominal
voltage
N
X(i)

Number of customers experiencing voltage sag with
magnitudes below X% due to measurement event i.
N
number of customers served from the section of the system
to be assessed
Despite being widely used, SARFI
X
only considers the
magnitude of voltage sag. Unfortunately, the magnitude value
maybe much greater than the actual number of tripped
electrical appliances, especially when the duration of sags is
small enough (less than a half second), such as for
transmission system in Vietnam where the total fault clearing
time of protection system is typically less than 5 to 7 cycles of
the mains frequency. To take the voltage sag duration into
account, SARFI
X

is developed into SARFI
CURVE-X
[5], [6]
which is defined below
N
N
SARFI
m
i
iX
XCURVE




1
'
)(
(2)
where
'
)(iX
N
:Number of customers tripped when experiencing
voltage sag with magnitudes below X% due to measurement
Prediction of Voltage Sag in The Transmission
System of Vietnam, A Case Study
Bach Quoc Khanh, Nguyen Hong Phuc
A
978-1-61284-788-7/11/$26.00 ©2011 IEEE

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event i.
If we plot voltage sag as a point with co-ordinates being its
magnitude and duration on the graph of the equipment
compatibility curve, SARFI
CURVE-X
corresponding to voltage
sags falling out of the equipment voltage tolerant area (Fig. 1)
will be obtained. So far, well known curves are CBEMA, ITIC
and SEMI [1]. Obviously, SARFI
CURVE-X
can provide a better
understanding of the influence of voltage sag on the operation
of electric equipment in electric networks. This paper presents
the method of calculating SARFI
X-CURVE
using ITIC and SEMI
curve (SARFI
ITIC-X
and SARFI
SEMI-X
) as case studies.

Fig 1. ITI curve for susceptibility of computer equipment
III. P
REDICTION OF VOLTAGE SAG IN
THE TRANSMISSION SYSTEM OF VIETNAM
A. Problem definition
The problem with stochastic prediction of voltage sag is
that it can only obtain the voltage sag performance of a
specific electric system by using data of causal events leading
to sags. In fact, more than 90% sag events are resulted from
short-circuits, hereby called faults, and it is possible to use
fault modelling and short-circuit calculation tools to simulate
and predict voltage sags in the power system. This work uses
the method of “fault position” [1] for voltage sag prediction in
the transmission systems with following significant steps
1. Modeling the fault distribution of the transmission system
of Vietnam – event modeling (Sub section B)
2. Calculating the short-circuit current and voltage sags at all
influenced load nodes – event indices (Sub section C)

3. Quantifying voltage sag frequency at load nodes (site
indices) and cumulating system sags with different
characteristics and obtaining SARFI
X
(system indices)
4. Cumulating system voltage sags that cause equipment to
trip and obtaining SARFI
CURVE-X
.
To obtain SARFI
X-CURVE
, the voltage sag duration that
depends on the fault clearing time of protective system should
be considered. This work takes the typical tripping time of
protective devices (instantaneous protective relay) and high
voltage circuit breakers currently used in the transmission
system in Vietnam into its calculation.
B. Fault Distribution Modeling and Assumptions
- Fault distribution modeling: Fault distribution modeling
considers the occurrence of all faults in the whole transmission
system of Vietnam that cover 500kV and 220kV networks.
The scope of the transmission system of Vietnam starts from
the points of energy receiving from generating centers or
interconnection points with the transmission system of South
China to load nodes that are step-down 220kV substations. An
individual fault (short-circuit) is characterized by a pair of
parameters: fault position, fault type and its occurrence is
assigned a fault rate. All faults with their assigned rate of
occurrence build up a fault distribution model. Following are
analyses of each fault characteristics for the transmission

system of Vietnam.
- Fault position: The fault can occur anywhere in the
transmission system including 500kV and 220kV networks.
Since load nodes of the transmission system are 220kV step-
down transformers, faults in 110kV networks and distribution
networks should not considerably impact on voltage sags in
transmission system because of large impedance of 220kV
step-down transformers. Faults at the power generating
sources should be included in the faults at the 220kV step-up
transformers. Therefore, this work only considers faults that
occur in the transmission system. According to [1], [3], [7],
basing on the concept of “area of vulnerability”, fault
positions should be generally chosen in the manner that a fault
position should be the representative for other nearby short-
circuit faults in a portion of network that cause voltage sags to
load nodes with the similar characteristics (similar
magnitudes). Voltage sag magnitude normally divides in 9
ranges : 0-0.1, 0.1-0.2,…, 0.8-0.9 p.u. Similar manitudes mean
the magnitudes that fall inside a same range of magnitude
above said. Faults in the transmission system are divided into
two groups. That are overhead line OHL faults (or faults on
branches) and transformer faults (faults on substations). In the
transmission system of Vietnam given in VI Master Plan [10]
for the year 2008, 63 substations 220kV will be seen as load
nodes for voltage sag assessment. The transmission system
(Fig. 2) includes the 500kV network (11 nodes as 500kV
substation and 17 branches of OHL with total length of
3246km) and the 220kV network (63 nodes as 220kV
substations and 103 branches of 220kV OHL with total length
of 6414km). In Figure 2, the number of 220kV substation is 51

that are under the management of National Power
Transmission Corporation (NPT). Other twelve 220kV
substations are under the management of power generation.
Therefore, transformer fault positions will be 11 for 500kV
substations and 63 for 220kV substations respectively. For
OHL faults, fault positions are selected depending on the
length of each branch. According to the above said principle
of fault position selection, we divide the line branches into
some segments and each segment is represented by one fault
position, normally at one of two ends of the line segment. For
220kV OHL, the line segment length shoud be from 10km to
40km depending on the line branch length. For 500kV OHL,
each line segment should be 50km. In this case study, fault
positions are selected at 76 locations for 500kV OHL and 169
locations for 220kV OHL. Therefore, there are 319 fault
positions in total.

SARFI
X-CURVE

qualified
SARFI
X-CURVE

disqualified
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Fig 2. The Transmission System of Vietnam in 2008
Vietnam National Power Transmission

Corporation
Total 500kV OHL length: 3441km
Total 220kV OHL length: 76541km
Number of 500kV substation: 11
Number of 220kV substation: 51
Total 500kV transformer capacity: 8756MVA
Total 500kV transformer capacity: 14761MVA
220/110/35kV
Mai Dong substation,
2x250MVA, Hanoi
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- Fault type: This calculation considers all types of short
circuit with well known contributory percentages of different
fault type are assumed as follows
Single phase to ground (SP-G): 65%
Two phase to ground (PP-G): 10%
Two phase together (P-P): 20%
Three phase to ground (3P-G): 5%
For the transmission system that requires high reliability
and stability, short-circuits are prone to permanent fault.
Therefore, in this work, transitory faults are not considered.
- Fault rate: The occurrence of short circuits depends on
many factors [3] and the rates of occurrence of different faults
(fault position, fault type) are normally not the same.
However, because, in reality, recorded fault data does not
consider detailed fault distribution, this work assumes that
fault distribution for each fault type follows uniform model

within each regions in Vietnam. For example, phase-to-ground
faults remain unchanged anywhere in the section of
transmission system within a region. The transmission system
is Vietnam is divided in four regions. The data of fault
performance recorded by NPT and its subsidiary agencies
(Power Transmission Companies, PTC) for 2008 is shown in
the Table 1 below.
TABLE 1. R
EGIONAL FAULT RATE PERFORMANCE
Regional Power
Transmission
Company
Line fault rate
(per km.year)
Substation
fault rate
(per year)
500kV 220kV
PTC1 (North) 0.00093 0.02504 0.0397
PTC2 (North Center) 0.00562 0.00536 0.0408
PTC3 (South Center) 0.00173 0.01279 0.0161
PTC4 (South) 0.0077 0.00808 0.0229
NPT 0.00407 0.01478 0.0306
It is noticeable that the fault rates stated in Table 1 are for
all four fault types as mentioned above. Therefore, for each
fault type, the fault rate should multiply by contributory
percentage of different fault types. For the fault that represents
OHL faults within a line segment, fault rate should be
calculated based on the length of the line segment.
- Selection of load nodes for voltage sag calculation: In the

transmission system, load nodes are 220kV substations
feeding to downstream 110kV and medium voltage networks.
The topology of transmission network is complicated and
many branches also have switching devices at both ends.
When a fault occurs on a certain branch (a line or a
transformer), the two switching devices at both ends of that
branch will trip and isolate it from the network. Therefore,
many load nodes normally experience voltage sags. Only the
loads on or nearby the fault position (for transformer fault)
suffers an interruption. So, voltage sags at all 63 load nodes
had to be considered in this work.
- System loading condition when faults occur: It is also
notable that for short-circuit calculation in the transmission
system where limited power sources are connects to, the short-
circuit current and voltage sags depend heavily on the pre-
fault loading condition when the fault occurs. The heavier the

True
False
True
False
True
False
True
Select the load node (among
63 nodes
)
for sa
g
calculation
START
Select the fault position
(
amon
g
319
p
ositions
)

Select the fault type
(
SP-G

,
PP-G
,
P-P
,
3P-G
)
Short-circuit
calculation and
determine voltage sag
magnitude at selected
load node by PSS/E
Fault distribution
modeling, determine
fault rate of the fault
under calculation
Calculate the frequency
of voltage sag at
the selected load node
Are
all fault type
selected ?
Are
all fault position
selected ?
Are
all load nodes
selected ?
Sag frequency
spectrum by

the fault under
calculation
(event index)
Sag frequency
spectrum at
selected load
node by all
faults
Sag frequency
spectrum at all
load nodes by
all faults
(site index)
SARFI
X

calculation
Check ITIC
curve ?
SARFI
X-CURVE

STOP
Fig 3.
Block diagram
of the problem
of prediction of
voltage sag in
the transmission
system of

Vietnam.
(system index)
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load on the system is, the higher short-circuit current will be
generated and the deeper voltage sags will be at load nodes.
Therefore, the most interested prefault loading condition is
obviously that of full loaded and this work performs the short-
circuit calculation in the maximum loading condition.
C. Short circuit calculation and voltage sag determination for
the transmission system of Vietnam
Short circuit calculation and voltage sag determination for
the whole transmission system of Vietnam is carried out by
program PSS/E (Power System Simulation for Engineering).
The block diagram of the calculation is depicted in Fig. 3.
- SARFI
X
calculation: With fault distribution modeling for
the transmission system proposed in Part B, this work
performs short-circuit calculation using the program PSS/E for
a certain individual fault (fault position, fault type) and then
voltage sag magnitude at a selected load node is calculated.
After assigning fault rate to this fault, the frequency of sag at
the selected load node resulted by this fault will be obtained.
By repeating this calculation for all other faults (fault position
and fault type), and gather them together, we obtains the
frequency spectrum of voltage sag with different magnitude
characteristics at the selected load nodes caused by all faults in

the transmission system. Fig. 4, Fig. 5 and Fig. 6 show an
example of voltage sag performance for an individual load
node (220kV Mai Dong substation in Hanoi, Fig. 3). Fig. 4
shows voltage sag frequency spectrum by sag magnitude
NEW














Fig 4. Voltage sag frequency spectrum (per year)
by fault types at load node 220kV Mai Dong substation

Fig 5. Voltage sag frequency spectrum (per year) for all fault
events at 220kV Mai Dong Substation, Hanoi, Vietnam
(per unit) intervals for different fault types. Fig. 5 is voltage
sag frequency spectrum for all fault types. Fig. 6 is the
cumulative voltage sag frequency.













Fig 6. Cumulative Voltage Sag Frequency (per year)
at 220kV Mai Dong Substation, Hanoi, Vietnam
For other load nodes, the calculation is similarly performed
and then we obtain voltage sag frequency spectrum of all other
load nodes. Finally, the average frequency spectrum per load
node is calculated and plotted on the Fig. 7 and SARFI
X
of the

whole transmission system of Vietnam is calculated as the
formula (1). The voltage sag performance of transmission
system – SARFI
X
is shown in Fig. 8.















Fig 7. Transmission system average voltage sag frequency
by magnitude characteristics

Fig 8. SARFI
X
and SARFI
CURVE-X
of
the transmission system of Vietnam
Sag Magnitude
(p.u)
Sag Magnitude
(p.u)
Sag Magnitude
(p.u)
SARFI
X

SARFI
ITIC-X

Sag Magnitude
(p.u)
SARFI
ITIC-0.7

SARFI
SEMI-X

SARFI
SEMI-0.5

Sag magnitude
(p
.u
)

SP-G
PP-G
P-P
3P-G
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- SARFI
ITIC-X
calculation: SARFI
X-CURVE
can be achieved by
taking fault clearing time of protective system into account.
For the transmission system of Vietnam, the primary functions
currently used for transformer protection is biased differential
protection using differential relays of SIEMENS (SIPROTEC
7UT613) or ALSTOM (MiCOM P340). For OHL line
protection, the primary functions currently in use are also the

differential protection as above said using the tele-
communication links of power line carrier or fibre-optical
ground wire integrated in power carrying lines or the distance
protection using differential relays of SIEMENS (SIPROTEC
7SA6) or ALSTOM (EPAC 3000, MiCOM P440). All those
protective relay system is of instantaneous tripping type that is
typically less than 100ms. The switching devices are almost
SIEMENS, SCHNEIDER or ABB products manufactured in
Europe with typical breaking time of 40ms for 500kV to 60ms
for 220kV circuit breakers. Besides the above mentioned
operating times of protective relays and circuit breakers,
additional time delays are also included for auxiliary relay
trips and operating time of tele-protection with total additional
operating time not exceeding two more cycles (20-24ms).
Therefore, the total fault clearing time is 160ms to 180ms that
defines the voltage sag duration. If posing this duration on the
ITIC curve, it’s obviously that only sags lower than 0.7 p.u.
will be out of load voltage tolerance and qualified for
SARFI
ITIC-X
. The upper 0.7 p.u. sags with duration defined by
the above said fault clearing time definitely fall inside the
voltage tolerance envelope and thus, they are not qualified as
SARFI
ITIC-X
. Therefore, SARFI
ITIC-X
is a part of SARFI
X
with

X lower than 0.7 p.u. as also shown on the SARFI
X
chart (Fig.
8). For X from 0.7 p.u to 0.9 p.u, the value of SARFI
ITIC-X

remains unchanged and equal to SARFI
ITIC-0.7
.
If we use SEMI curve for assessment of sag duration, it is
noticeable that there is a small difference between ITIC curve
and SEMI curve for X from 0.5 cycle to 10 cycles (Fig. 9).













Figure 9. The difference between ITIC curve and SEMI curve.
Within this range, ITIC ridethrough voltage is 0.7 p.u whereas
this voltage level for SEMI F47 is just 0.5 p.u. Therefore, with
the total fault clearing time (160ms to 180ms) for the
transmission system in Vietnam, only voltages sag with X

lower than 0.5 p.u are qualified for SARFI
CURVE-X
using the
SEMI curve (SARFI
SEMI-X
). With X greater than 0.5 p.u,
voltage sags fall inside SEMI’s ridethorugh area and not
qualified for SARFI
SEMI-X
. So, for X from 0.5 p.u to 0.9 p.u,
the value of SARFI
SEMI-X
remains unchanged and equal to
SARFI
ITIC-0.5
. SARFI
SEMI-X
is also shown on Fig 8.
D. Result Analysis
From the results, there’re some following remarks:
- The SARFI
X
and SARFI
CURVE-X
values obtained from this
calculation are useful for utilities as a benchmark for reducing
the frequency of fault for solving the problem of voltage sag.
This result also helps customers know the voltage sag
performance and choose suitable location for less voltage sag
frequency.

- The frequency of voltage sag as the result of an individual
fault type is proportional to fault rate of that fault type for
shallow sags (Fig. 4).
- Shallow sags (0.7-0.9 p.u) feature a rather high frequency
while the frequency of deep sags is very small. Furthermore,
the frequency of voltage sag with X lower than 0.9 for either
the 220kV Mai Dong substation (about 33 times, Fig. 5) and
the system average load node (about 22 times, Fig. 7) is also
khanh

Fig 9. Voltage sag frequency of selective load nodes
(220kV substations) throughout of Vietnam

Sag magnitude
(p.u)
Sag magnitude
(p.u)
Sag magnitude
(p.u)
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